TY - JOUR
T1 - Asymptotic Formulas for Thermography Based Recovery of Anomalies
AU - Habib Ammari, Anastasia Kozhemyak & Darko Volkov
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 18
EP - 42
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6014.html
KW - Thermography, imaging, asymptotic formulas, small anomalies, direct imaging algorithms, half-space problem.
AB - <p style="text-align: justify;">We start from a realistic half space model for thermal imaging, which we
then use to develop a mathematical asymptotic analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their
rough features. With this way our proposed algorithms are stable against measurement
noise and geometry perturbations. Based on rigorous asymptotic estimates, we first
obtain an approximation for the temperature profile which we then use to design noniterative detection algorithms. We show on numerical simulations evidence that they are
accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.</p>